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Angular Measure

Size and scale are often specified by measuring lengths and angles. The concept of lengthmeasurement is fairly intuitive to most of us. The concept ofangular measurementmay be less familiar, but it too can become second nature if you remember a few simple facts.

A full circle contains 360 degrees (360°). Thus, the half-circle that stretches from horizon to horizon, passing directly overhead and spanning the portion of the sky visible to one person at any one time, contains 180°.

Each 1° increment can be further subdivided into fractions of a degree, called arc minutes.There are 60 arc minutes (written 60´) in one degree. (The term "arc" is used to distinguish this angular unit from the unit of time.) Both the Sun and the Moon project an angular size of 30 arc minutes on the sky. Your little finger, held at arm’s length, does about the same, covering about a 40' slice of the 180° horizon-to-horizon arc.

An arc minute can be divided into 60 arc seconds (60´´). Put another way, an arc minute is 1/60 of a degree, and an arc second is 1/60 x 1/60 = 1/3600 of a degree. An arc second is an extremely small unit of angular measure—it is the angular size of a centimeter-sized object (a dime, say) at a distance of about two kilometers (a little over a mile).

The accompanying figure illustrates this subdivision of the circle into progressively smaller units.

Don’t be confused by the units used to measure angles. Arc minutes and arc seconds have nothing to do with the measurement of time, and degrees have nothing to do with temperature. Degrees, arc minutes, and arc seconds are simply ways to measure the size and position of objects in the universe.

The angular size of an object depends both on its actual size and on its distance from us. For example, the Moon, at its present distance from Earth, has an angular diameter of 0.5°, or 30´. If the Moon were twice as far away, it would appear half as big—15´ across—even though its actual size would be the same. Thus, angular size by itself is not enough to determine the actual diameter of an object—the distance must also be known. We return to this topic in more detail in More Precisely 1-3.